A new MITC4+ shell element

We presented in Ko et al. (2016) an MITC4+ shell element that shows a much improved convergence behavior when compared to the widely used MITC4 (Dvorkin and Bathe, 1984) shell element. However, the element does still not show optimal convergence behavior when used in distorted meshes in the analysis of some shell problems. In the present paper, we establish a new MITC4+ shell element which shows significantly improved and indeed an almost optimal convergence behavior. In this new continuum mechanics-based shell element, the shear locking is alleviated using the well-known assumed transverse shear strain field of the original MITC4 shell element and the membrane locking is alleviated using a new assumed membrane strain field. The new MITC4+ shell element passes all basic tests: the isotropy, zero energy mode and patch tests. The excellent performance of the shell element is demonstrated through convergence studies in the solution of well-selected behavior-encompassing shell benchmark problems.